Do you use “math” and “deductive reasoning” to refer to distinct activities?
Inference rules, axioms, language?
I’ve heard people say things like, “The world is math”, but it never seemed particularly coherent to me. Sometimes I’d assume they meant, “Inference systems with mathematical languages make useful predictions about my empirical experience.”
But now I’m favoring the interpretation that experience is purely formal/syntactic with no semantic component. There is no additional meaning beyond (or behind) appearance.
If the formal/syntactic appearance is how leads to new possibilities involving more formal/syntactic appearances, then that is its meaning.
But isn’t that just some hidden metaphysical structure? That is, it’s unavailable as formal appearance?
But a lot of real world "logic" (decision theory, etc) is statistical in nature, often with a big inductive component and often based on "axioms" that only approximate the real world.
In other words, the field of Analytic Philosophy, when not using the proper amount of math and statistics (especially Bayesian statistics) tend to either lead to doubting everything (if they know what things they do not know) or drawing bad conclusions (if treating their axiomatic assumptions as absolute truths)
They have similar problems with science, and maybe Physics in particular, because of the abstraction of modern physics. By interpreting statements made by some physicist too literally, they may (falsely) end up with conclusions that go way beyond the domain of validity of the original statement.
Imho, Philosophy is fine as a side-project for people in academia, but I think philosphers who do not study math, science, psychology, etc at a level comparable to their philosophy work are at risk of ending up in lala-land.
I would estimate that if someone studies only philosophy in college, they will reach a point after about 1 year where their knowledge of philosophy come to a point that requires more understanding of math, science etc than they had when they started. Kind of like a physicist that doesn't take college level math.